用关联函数乘积态近似强关联自旋和费米子波函数
Approximating strongly correlated spin and fermion wavefunctions with correlator product states
摘要：
我们探讨了关联函数乘积态对任意维关联波函数的近似。我们发现，他们包括许多有趣的国家，包括Laughlin的量子霍尔波函数，Huse和Elser的挫折自旋状态，Kitaev的复曲面代码。我们进一步建立他们的关系，常见的家庭变分波函数，如矩阵和张量积状态和共振价键态。对海森堡模型和无自旋哈伯德模型的计算表明，关联函数乘积态既能捕获二维关联（与系统宽度无关），也能捕获非平凡的费米子关联（没有符号问题）。在一维模拟中，关联函数的产品状态出现与矩阵产品状态具有可比数量的变分参数的竞争，这表明他们可能最终提供了一条路线，实际上概括的密度矩阵重整组更高的维度。
英文摘要：
We explore correlator product states for the approximation of correlated wavefunctions in arbitrary dimensions. We show that they encompass many interesting states including Laughlin's quantum Hall wavefunction, Huse and Elser's frustrated spin states, and Kitaev's toric code. We further establish their relation to common families of variational wavefunctions, such as matrix and tensor product states and resonating valence bond states. Calculations on the Heisenberg and spinless Hubbard models show that correlator product states capture both two-dimensional correlations (independent of system width) as well as non-trivial fermionic correlations (without sign problems). In one-dimensional simulations, correlator product states appear competitive with matrix product states with a comparable number of variational parameters, suggesting they may eventually provide a route to practically generalise the density matrix renormalisation group to higher dimensions.
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